std::philox_engine is a counter-based random number engine.

[edit]Template parameters

If any of the following values is nottrue, the program is ill-formed:

• sizeof...(consts)== n
• n==2|| n==4
• 0< r
• 0< w&& w<=std::numeric_limits<UIntType>::digits

[edit]Generator properties

In the following description, let\(\scriptsize Q_i \)Qi denote theith element of sequenceQ, where the subscript starts from zero.

Thesize of the states ofphilox_engine is\(\scriptsize O(n)\)O(n), each of them consists of four parts:

• A sequenceX ofn integer values, where each value is in[​0​, 2w
).

• This sequence represents a large unsigned integer counter value\(\scriptsize Z=\sum_{j=0}^{n-1} X \cdot 2^{wj} \)Z=∑n-1
  j=0X⋅2wj
  of\(\scriptsize n \cdot w \)n⋅w bits.

• A sequenceK ofn/2 keys of typeUIntType.
• A bufferY ofn produced values of typeUIntType.
• An indexj inY buffer.

Thetransition algorithm ofphilox_engine (\(\scriptsize TA(X_i) \)TA(Xi)) is defined as follows:

• Ifj is notn-1, incrementsj by1.^[1]
• Ifj isn-1, performs the following operations:^[2]

1. Generates a new sequence ofn random values (see below) and stores them inY.
2. Increments the counterZ by1.
3. Resetsj to​0​.

Thegeneration algorithm ofphilox_engine is\(\scriptsize GA(X_i)=Y_j \)GA(Xi)=Yj.

1. ↑In this case, the next generation algorithm call returns the next generated value in the buffer.
2. ↑In this case, the buffer is refreshed, and the next generation algorithm call returns the first value in the new buffer.

[edit]Generating random values

Random values are generated from the following parameters:

• the number of roundsr
• the current counter sequenceX
• the key sequenceK
• the multiplier sequenceM
• the round constant sequenceC

The sequencesM andC are formed from the values from template parameter packconsts, which represents the\(\scriptsize M_k \)Mk and\(\scriptsize C_k \)Ck constants as[\(\scriptsize M_0 \)M0, \(\scriptsize C_0 \)C0, \(\scriptsize M_1 \)M1, \(\scriptsize C_1 \)C1,... , ..., \(\scriptsize M_{n/2-1} \)Mn/2-1, \(\scriptsize C_{n/2-1} \)Cn/2-1].

Random numbers are generated by the following process:

1. Initializes the output sequenceS with the elements ofX.
2. Updates the elements ofS forr rounds.
3. Replaces the values in the bufferY with the values inS.

[edit]Updating the output sequence

For each round of update, an intermediate sequenceV is initialized with the elements ofS in a specified order:

Given the following operation notations:

• \(\scriptsize \mathsf{xor} \)xor, built-inbitwise XOR.
• \(\scriptsize \mathsf{mullo} \)mullo, it calcuates the low half of modular multiplication and is defined as\(\scriptsize \mathsf{mullo}(a,b,w)=(a \cdot b) \mod 2^w \)mullo(a,b,w)=(a⋅b) mod 2w
  .
• \(\scriptsize \mathsf{mulhi} \)mulhi, it calcuates the high half of multiplication and is defined as\(\scriptsize \mathsf{mulhi}(a,b,w)=\left\lfloor (a \cdot b)/2^w \right\rfloor \)mulhi(a,b,w)=⌊(a⋅b)/2w
  ⌋.

Letq be the current round number (starting from zero), for each integerk in[​0​, n/2), the elements of the output sequenceS are updated as follows:

• \(\scriptsize X_{2 \cdot k}=\mathsf{mulhi}(V_{2 \cdot k},M_k,w)\ \mathsf{xor}\ ((K_k+q \cdot C_k) \mod 2^w)\ \mathsf{xor}\ V_{2 \cdot k+1} \)X2⋅k=mulhi(V2⋅k,Mk,w) xor ((Kk+q⋅Ck) mod 2w
  ) xor V2⋅k+1
• \(\scriptsize X_{2 \cdot k+1}=\mathsf{mullo}(V_{2 \cdot k},M_k,w) \)X2⋅k+1=mullo(V2⋅k,Mk,w)

[edit]Predefined specializations

The following specializations define the random number engine with two commonly used parameter sets:

[edit]Nested types

[edit]Data members

[edit]Member functions

[edit]Non-member functions

[edit]Notes

[edit]Example

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